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The building blocks of Hudson-Parthasarathy quantum stochastic calculus startwith Weyl operators on a symmetric Fock space. To realize a relativisticallycovariant version of the calculus we construct representations of Poincaregroup in terms of Weyl operators on suitably constructed, Bosonic or Fermionicbased on the mass and spin of the fundamental particle, Fock spaces. We proceedby describing the orbits of homogeneous Lorentz group on R4 and build fiberbundle representations of Poincar\'e group induced from the stabilizersubgroups (little groups) and build the Boson Fock space of the Hilbert spaceformed from the sections of the bundle. Our Weyl operators are constructed onsymmetric Fock space of this space and the corresponding annihilation,creation, and conservation operators are synthesized in the usual fashion inrelativistic theories for space-like, time-like, and light-like fields. Weachieve this by constructing transitive systems of imprimitivity(second-quantized SI), which are dynamical systems with trajectories dense inthe configuration space, by induced representations. We provide the details ofthe field operators for the case of massive Bosons as the rest are similar inconstruction and indicate the ways to construct adapted processes paving wayfor building covariant quantum stochastic calculus.

Covariant Quantum Fields via Lorentz Group Representation of Weyl Operators